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wm.annisI got this fractal system switched over to the refactored/rewritten version of my Common Lisp library. For some reason, this is noticeably faster than in the original library (which has not always been the case).<a href="https://mastodon.art/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractal</a> <a href="https://mastodon.art/tags/CommonLisp" class="mention hashtag" rel="nofollow noopener" target="_blank">#CommonLisp</a> <a href="https://mastodon.art/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a>

Dani Laura (they/she/he)In the following artworks the corners of the polygonal lines are rounded. <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/algorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#algorithmicArt</a> <a href="https://mathstodon.xyz/tags/AbstractArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AbstractArt</a>

Dani Laura (they/she/he)These artworks are based on a generalization of Lucas sequences for complex numbers, defined as: Z(0) = 1 Z(1) = 1 or i Z(n) = shrink( e^(iθ)·Z(n-1) + Z(n-2) )Where shrink() is a function which decreases a complex number into the two-unit square or the unit circle centered at the origin. In these works I use three different versions, based on taking out the integer part of the real and imaginary parts (or the integer part minus 1), or of the modulus of the number in polar form.Figure 1 depicts the 128 values walk using θ = π/5 and Z(1) = i, and the shrinking function which takes out the integer part of the real and imaginary parts.In the three artworks that follow, the lines connecting successive values toggle between being drawn or not. See the alt text for more information related to the artworks. <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/algorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#algorithmicArt</a> <a href="https://mathstodon.xyz/tags/AbstractArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AbstractArt</a>

Laurent Houdard<a href="https://pixelfed.social/discover/tags/generativeart?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#generativeart</a> <a href="https://pixelfed.social/discover/tags/codeart?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#codeart</a> <a href="https://pixelfed.social/discover/tags/algorithmicart?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#algorithmicart</a> <a href="https://pixelfed.social/discover/tags/abstract?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#abstract</a> <a href="https://pixelfed.social/discover/tags/monochrome?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#monochrome</a> <a href="https://pixelfed.social/discover/tags/blackwhite?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#blackwhite</a>

Dani Laura (they/she/he)Fractal with decagonal symmetry for <a href="https://mathstodon.xyz/tags/FractalFriday" class="mention hashtag" rel="nofollow noopener" target="_blank">#FractalFriday</a> . <a href="https://mathstodon.xyz/tags/fractal" class="mention hashtag" rel="nofollow noopener" target="_blank">#fractal</a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/algorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#algorithmicArt</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a>

Steven Dollins80 vertices in 2-fold dihedral symmetry has triangle strips of 4 different lengths.<a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

Steven DollinsWe can also get 80-vertex tetrahedral symmetry with a more "traditional" arrangement of 12 pentagons and the rest hexagons.<a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

Steven DollinsHere is an 80-vertex sphere in tetrahedral symmetry with 24 valence-7 vertices.<a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

wm.annisStill rewriting the algorithmic art library I wrote in <a href="https://mastodon.art/tags/CommonLisp" class="mention hashtag" rel="nofollow noopener" target="_blank">#CommonLisp</a> during the height of COVID. I can't say I've managed to make it too much faster, but it *is* easier to use. The canvas mottling code is so much shorter now, and ready to go.Drawing on a flat canvas can be boring.The mottled texturing is managed by just doing a bunch of random walks until the pen leaves the scene. Each one has a color *close* to the original canvas background.<a href="https://mastodon.art/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a>

Jeff PalmerCompleted this painting recently. Not sure if I've mentioned this, but I've transitioned to a mode where I create computer algorithms that generate images, which I then paint by hand. I find the process of mapping rigid computer-based processes to the messy real world to be an extremely satisfying approach.<a href="https://genart.social/tags/Art" class="mention hashtag" rel="nofollow noopener" target="_blank">#Art</a> <a href="https://genart.social/tags/Artist" class="mention hashtag" rel="nofollow noopener" target="_blank">#Artist</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/Painting" class="mention hashtag" rel="nofollow noopener" target="_blank">#Painting</a> <a href="https://genart.social/tags/AcrylicPainting" class="mention hashtag" rel="nofollow noopener" target="_blank">#AcrylicPainting</a>

Dani Laura (they/she/he)Nature promotes diversity, don't be anti-nature. Good <a href="https://mathstodon.xyz/tags/Stonewall" class="mention hashtag" rel="nofollow noopener" target="_blank">#Stonewall</a> uprising anniversary! (28th of June) This piece was created as follows: each element was generated based on a prime number from 2 upwards, specifically the first six decimal places of its square root. The first four decimals defined the shape, the next two the colours. Shapes are based on the properties of the plastic ratio (plastic as in plastic arts, not the infamous material), a lesser-known ratio with many interesting properties. As can be seen in the second picture, there are several ways to connect the ends of a quarter of a unit circle as a sequence of quarter sectors with radii the inverse powers of this ratio, up to the fifth. There are exactly ten possibilities disregarding sector rotations, so each one can represent one decimal place (third picture), and four sides make up the whole shape. For the colours, each decimal represents one of ten colours; inside they are renderend lighter and outside darker. Lastly, the grey background was generated using the Halton sequences of 2, 3 and 5.<a href="https://mathstodon.xyz/tags/pride" class="mention hashtag" rel="nofollow noopener" target="_blank">#pride</a> <a href="https://mathstodon.xyz/tags/LGBTQ" class="mention hashtag" rel="nofollow noopener" target="_blank">#LGBTQ</a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/algorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#algorithmicArt</a> <a href="https://mathstodon.xyz/tags/AbstractArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AbstractArt</a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#geometry</a>

NeussWaveSieht nach nicht viel aus, ist aber das Ergebnis von einer Woche Arbeit. Ich lerne nun Python und das ist mein erstes Projekt: Ein Framework um algorithmische Kunst zu produzieren. Das hier wird von 2 Filtern gemacht.Aktuell unterstützt es nur Zufallszahlen als Input, als nächstes kommt aber Musik dazu.Ich glaube, zuerst mag ich aber Fractal Flames von Scott Draves einbauen 🤔 <a href="https://neuss.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://neuss.social/tags/GenerativeArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#GenerativeArt</a> <a href="https://neuss.social/tags/DigitalArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#DigitalArt</a> <a href="https://neuss.social/tags/Art" class="mention hashtag" rel="nofollow noopener" target="_blank">#Art</a> <a href="https://neuss.social/tags/Python" class="mention hashtag" rel="nofollow noopener" target="_blank">#Python</a> <a href="https://neuss.social/tags/Programming" class="mention hashtag" rel="nofollow noopener" target="_blank">#Programming</a>

Steven DollinsTetrahedral symmetry requires that a general point be in a set of 12 -- on each of the 4 faces in each of 3 orientations. You can also add 4 points at the vertices, 4 at each face center, or 6 at each edge center. Combined, any even number of points >= 4 can be arranged with tetrahedral symmetry, albeit not always evenly.Here is 50 points in tetrahedral symmetry which requires that some of them have valence 7.<a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

Steven Dollins50 vertices arranged in D6 symmetry is interesting in that it forms two different but close in length triangle strips -- one following the longitudes and the other the latitudes.<a href="https://genart.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

Steven DollinsAnd 22 vertices can also arrange with 2-fold cylindrical symmetry that runs all the pentagons together into one long strip. It produces one long triangle strip and three short ones.<a href="https://genart.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

Steven Dollins22 vertices can also arrange with 2-fold dihedral symmetry with two strips of six pentagons each separated by a single loop of 10 hexagons. The triangulation has two long triangle strips and two short ones.<a href="https://genart.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

Steven Dollins40 vertices in tetrahedral symmetry gives a mix of the two with 4 strips that wrap twice and three that only wrap once.<a href="https://genart.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

Steven Dollins22 vertices can also have tetrahedral symmetry, but now only have four strips that each wrap the sphere twice.<a href="https://genart.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

Steven Dollins16 vertices gives a triangulation with tetrahedral symmetry. It has 7 triangle strips.<a href="https://genart.social/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#TilingTuesday</a> <a href="https://genart.social/tags/AlgorithmicArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#AlgorithmicArt</a> <a href="https://genart.social/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#CreativeCoding</a> <a href="https://genart.social/tags/Processing" class="mention hashtag" rel="nofollow noopener" target="_blank">#Processing</a> <a href="https://genart.social/tags/glsl" class="mention hashtag" rel="nofollow noopener" target="_blank">#glsl</a> <a href="https://genart.social/tags/shaders" class="mention hashtag" rel="nofollow noopener" target="_blank">#shaders</a>

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